Ocean currents are actually very important, as you state. The flow or flux of energy is far more important then temperature readings. Especially atmospheric temperatures which represent very minor proportions of the total energy flux. Apes holding thermometers have no clue what they are doing. If there was no water current and all Oceans were stagnant, the equatorial surface layers would be very warm and the deeper and polar regions very cold. Basically a constant El Nino. Solar energy fluxing from ocean surface to atmosphere.
The super continent periods had some really nasty climate conditions due in part to the stagnant currents. When the land masses broke up, there was frequently an explosion of live forms.